1. Field of the Invention
This invention relates in general to a method of direct-sequence spread-spectrum communications, and in particular to a method of direct-sequence spread-spectrum communications addressing inter-chip and/or inter-symbol interferences due to multi-path arrivals in an acoustic channel.
2. Description of the Related Art
Underwater acoustic communications are band-limited due to the increased attenuation at higher frequencies. Phase coherent underwater acoustic communications provide an efficient use of the limited bandwidth and have received a great deal of attention recently. Direct-sequence spread-spectrum (“DSSS”) signaling uses phase coherent signals, where the information symbols are coded/multiplied with a code sequence, commonly known as chips. The signals are processed at the receiver using the code sequence as a matched filter to extract the information symbols. Two advantages of DSSS signals are: (1) multiple access communications between the different users using different code sequences which are almost orthogonal to each other, and (2) communications at low signal levels (e.g., below the noise level) to avoid detection and interception by an unfriendly party. For the former, the focus is on the separation of messages (i.e., interference suppression) using code orthogonality. For the latter, the focus is on the signal enhancement for the intended receiver using the processing gain of the matched filter.
The problem for DSSS communications in an underwater acoustic channel is the multipath arrivals which create severe inter-chip and inter-symbol interferences. As the decision to feedback equalizer (“DFE”) has been successfully applied to phase coherent signals, the same approach has been adapted for DSSS communications. To achieve precise symbol synchronization and channel equalization, high signal-to-noise ratio (“SNR”) signals are required. Similarly, a RAKE receiver has been applied to differentially coherent signals when multipath arrivals have been identified. A coherent RAKE receiver has been coupled with an extended Kalman-filter based estimator for the channel parameters. Such approaches have not addressed the difficulty of acquisition/tracking for real data at low input-SNRs since the accuracy of symbol synchronization degrades significantly with decreasing SNR.
The interest in low-input-SNR acoustic communications lies in some practical applications. Acoustic signals much weaker than the ambient noise (e.g., −8 dB SNR within the signal band) are difficult to detect by an un-alerted listener. Noise-like signals are difficult to decode without a prior knowledge of the structure of the signal. Communications with low-input-SNR signals at the receiver are said to provide a low probability of interception (“LPI”) and low probability of detection (“LPD”). The probabilities of detection and interception are a function of the input-SNR. Naturally, when the interceptor is close to the transmitter, the communication may no longer be LPI/LPD due to the increasing SNR.
To be able to decode symbols from low-input-SNR signals, the symbol energy must be brought above the noise by signal processing. The ratio of the output symbol SNR over the input-SNR is called the processing gain (“PG”). Using the DSSS method, the received data are de-spread by a correlator (e.g., a matched filter), which correlates the received data with the transmitted code sequence. The de-spreading provides a matched filter gain (“MFG”) for the signal, equal, in theory, to the time-bandwidth product of the spreading code. No MFG is expected for random noise, e.g., additive white Gaussian noise (“AWGN”). Thus theoretically, PG is determined by the MFG; they differ by a small amount in practice.
The DSSS approach uses code “orthogonality” to minimize interference between symbols as well as between users. The code orthogonality requires that the code sequence is almost orthogonal to any of the cyclically-shifted code sequences and to the code sequence of other users. With orthogonality, the matched filtered output yields a low sidelobe level and thus ensures minimum interference. It assures accurate symbol synchronization. However, the orthogonality of the codes is severely degraded in an underwater channel due to the rich multipaths creating inter-chip interference. To mitigate the multipath, DFE and RAKE receiver have been proposed, but both require high input-SNR and synchronization at the chip level, and are not designed for communications with low input-SNRs.
Another approach to mitigate the multipath effect is referred to as passive-phase conjugation (“PPC”), which uses a linear filter based on the estimation of the channel impulse-response. For DSSS communications, this method requires only “coarse” synchronization at the symbol level and is suitable for communications at low input-SNRs. Coarse, in this context, means imprecise, such that accuracy is of the order of several chips. The standard PPC method estimates the channel impulse-response from a probe signal transmitted before the communication packet. The standard PPC method does not work well at low input-SNRs such as around 17 kHz. Even at high input-SNRs, the PPC method fails because it does not account for the temporal variation of the channel, when the channel coherence time is significantly shorter than the packet length. The PPC method requires that the channel coherence time is approximately equal or longer than the packet length. In actuality, at high (e.g., >10 kHz) frequencies, the channel coherence time is less than 0.2 seconds, while the packet length is approximately 5-20 seconds. For underwater acoustic communications, the symbol phase is path dependent and the overall phase generally changes rapidly with time from symbol to symbol except for some specific environments (e.g., the Arctic) where the ocean remains stationary. The challenge for DSSS underwater communications is how to remove/compensate the phase fluctuations in a dynamic ocean when the phase change is non-negligible and disrupts the ability to communicate using phase-shift-keying.
It is noted that the PPC normally requires an array of receivers. Practical systems usually allow only a small number of receivers. The advantage of DSSS is that a single receiver is often sufficient. In this context, PPC is basically a matched filter, or a correlator. Since the filter uses the channel impulse-response, the method is still referred to as PPC. Obviously, the method can be applied to an array of receivers with the added benefit of minimal signal fading and reduced phase variance.
FIG. 3a shows the symbol-constellations-plot of the complex symbol amplitudes determined from the dominant arrival path (i.e., the peaks of the matched filter output in FIG. 2a). The true symbols are located at +1 and −1. The received symbols in FIG. 3a are unduly scattered and a large number of the symbols are in error. The phase wander is caused by the propagation medium; the symbol phases are significantly modified by the signal propagation in a time varying medium. FIG. 3b shows the phase error between the received symbols and the transmitted symbols. Symbols which have a phase error beyond ±90 degrees are in error.
In general, the symbol phase error is path-dependent, as multipaths travel through different water columns and have different path lengths. To mitigate the multipath-induced symbol distortions, a channel equalizer is needed. Using DFE jointly with a phase-locked loop (“PLL”) is computationally intensive and requires a high input-SNR (e.g., normally greater than 10-15 dB).
Another method used to mitigate the multipath effect is the PPC mentioned above, also known as the passive time reversal method, which uses the channel impulse-response estimated from the probe signal, or the first symbol, as the matched filter; it can be viewed as a basic time-invariant linear equalizer. One notes that the matched filter output, FIG. 2a, can be expressed mathematically as
                              r          ⁡                      (            t            )                          =                                            ∑              n                        ⁢                                                            h                  n                                ⁡                                  (                                      t                    -                    nT                                    )                                            ⁢                              S                n                            ⁢                              G                ⁡                                  (                                      t                    -                    nT                                    )                                            ⁢                              m                ⁡                                  (                  t                  )                                                              +          N                                    (        1        )            where Sn is the n-th transmitted symbols (Sn=±1 for binary symbols), hn is the channel impulse associated with the n-th symbol, G is a rectangle window which is zero for t<nT−T/2 and t>nT+T/2 and N denotes the noise. In Eq. (1), m(t) is the autocorrelation function of the spreading code, which, in the ideal case, yields M (the number of chips) at the center of the correlator and one elsewhere.
The PPC processor convolves the correlator output, Eq. (1), with the time-reversed, complex-conjugated channel impulse-response estimated at t=0, denoted by ĥ0. For simplicity (in order to illustrate the principle of the processing algorithms), the hat over h0 will be dropped in the equations below, treating the estimated impulse-response as the same as the true impulse-response and leaving the channel estimation error to the numerical estimator. Using PPC, the n-th symbol is estimated from the peak ofŜn=0*{circle around (x)}(hnSn+N)=(h0**hn)Sn+Nh  (2)where the superscript * denotes the complex conjugation, the inverse-arrow above the impulse-response denotes the time-reversal operator, {circle around (x)} denotes the convolution operator and * denotes the correlation operator. Note that the convolution of a time-reversed function with another function is the same as the correlation of the function with the other function. In Eq. (2), Nh denotes the filtered noise: Nh=h0*N.
The PPC filter (h0) provides a means to combine the multipath arrivals of the signal coherently. For a time-invariant environment, it is expected to provide a higher gain than the incoherent RAKE receiver. For low input-SNR (e.g., around 17 KHz) data, this standard PPC method performs poorly. The symbol constellation plot and the phase error plot are basically the same as that shown in FIGS. 3a and 3b respectively except for the first 8 symbols, which have near-zero phase error. The close similarity between PPC and that based on the dominant path arrival is a manifestation of the fact that the impulse-response is dominated by one major arrival. In view of the above, Applicant concluded that for such an environment, the standard PPC does not work.